Abstract: In this article, stiffness tensor of materials is derived for fibrous composites of aerial materials, based on the compatibility relation of deformation of fibers in matrices and the strain energy density of the fibrous composites. Principal mechanical properties of the stiffness matrix are investigated to derive the relations between material stiffness and matrix stiffness, and between stiffness of fibers and their orientations. Moreover, fundamental formulas and methods for stiffness design of laminated and spatially distributed fibrous composites are provided. Finally, examples are given to illustrate how to use the design formulas and compare them with other theories and experimental data. The research results indicate that after considering the stiffness discount due to imperfect of manufacture technology, the proposed formulas and methods can be applied to the optimization of design with fibrous composites.

Key words: fibrous composites, stiffness matrix, stiffness design, mechanical properties, engineering application